2001 AIME I Problem 2

A finite set \mathcal{S} of distinct real numbers has the following properties: the mean of \mathcal{S}\cup\{1\} is 13 less than the mean of \mathcal{S}, and the mean of \mathcal{S}\cup\{2001\} is 27 more than the mean of \mathcal{S}. Find the mean of \mathcal{S}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.